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Download as PDF; Printable version; In other projects ... Pages in category "Conic sections" The following 51 pages are in this category, out of 51 total ...
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
The ellipse, parabola, and hyperbola are viewed as conics in projective geometry, and each conic determines a relation of pole and polar between points and lines. Using these concepts, "two diameters are conjugate when each is the polar of the figurative point of the other."
The circle is an instance of a conic section and the nine-point circle is an instance of the general nine-point conic that has been constructed with relation to a triangle ABC and a fourth point P, where the particular nine-point circle instance arises when P is the orthocenter of ABC.
In homogeneous coordinates, each conic section with the equation of a circle has the form + + = It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane) the points I(1: i: 0) and J(1: −i: 0).
Translations added to this section should be free of copyright claims (either CC0 or public domain). circle ≅ circle (Q17278) circle ellipse ≅ ellipse (Q40112) ellipse parabola ≅ parabola (Q48297) parabola hyperbola ≅ hyperbola (Q165301) hyperbola
Download QR code; Print/export ... Coordinate-free treatment; Four-dimensional space; ... Conic section. Focus; Circle. List of circle topics;
A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e. If 0 < e < 1 the conic is an ellipse, if e = 1 the conic is a parabola, and if e > 1 the conic is a hyperbola.